We first initialized a cluster at a random position in the Galaxy, and set its velocity as the Galactic co-rotation speed plus a random peculiar velocity. We chose to draw the direction of the peculiar velocity isotropically in the sphere, and its magnitude is drawn from a Gaussian distribution with a 15 km.s\(^{-1}\) width according to the typical velocity dispersion in clusters reported by [1]}. The cluster effective radius was randomly picked following the distribution in radii in our sample of open clusters.
